GPAs and test scores are not absolute requirements. That is, beyond a certain point, they cease to matter (basically, the law of diminishing returns applies quite well). For example, of the hundreds of current and former admissions officers that I’ve spoken to or which work at our company, never has one said (and I’ve asked) that there is any meaningful difference between a 2300 and a 2400, or a 3.95 and a 4.0 – other than as a tie breaker between two essentially identical students.

In your case, you are right that your GPA is low for these schools, which have, respectively, average GPAs of (these are from my own personal notes, and I have not had a chance to cross-reference these numbers. They are all taken from reputable sources, but I’m only using them for the purpose of explanation):
MIT – 3.9 – 4.0
Stanford – 4.18 (weighted, see more here: Stanford University)
Harvard – 4.04
Princeton – 3.9 (I suspect this is inaccurate, based both on the source and the number itself)
Brown: 3.82-4.0 (25th-75th percentile)

What this all means is that, rather than seeing scores and GPAs as important in and of themselves, you should see them as the admissions office sees them – proxies for important information about you.

The SAT, for example, is intended to measure your likely performance in freshman year of college (which it doesn’t actually do, but is nonetheless used).

Grades can be seen as a measure of both academic talent, as well as diligence. Together, they speak to the work ethic, passion, and possible future performance of an individual applicant.

So what does your low GPA say about you? Based on the rest of what you have provided about yourself, an admissions officer might assume that while you are very talented, you are either not hard-working enough, or are not disciplined enough to work hard when you aren’t working on something which you choose yourself. In either case, these aren’t superb inferences for them to draw about you.

Thus, the rest of your application will need to address two things very well:
1. (every applicant needs to address this) why are you unique, and what can you offer the next class of X university that other students cannot. Some of your activities are pretty unique and sound very impressive. Chances are you won’t have too much trouble here.

2. Why should your GPA not be a serious concern to the admissions office? This is tough. Chances are, the best way to fight this perceived weakness is with recommendation letters that tackle the subject head-on. Teachers willing to attest to the fact that your GPA is not representative of what the admissions officer assumes that it represents (diligence, academic talent, etc.), will go a long way. Even better if that teacher can talk about other students they have recommended to these schools, who have attended or gotten accepted, and how you stack up compared to them (obviously, this only helps if the answer isn’t ”you are worse”).

Ultimately, I think you face an uphill battle – as do all applicants to these schools – but that you are far from a lost cause. If you work hard thinking about how you will be perceived in the admissions office (given all of your information and credentials), what characteristics the admissions office is searching for, and how to address your perceived shortcomings in those areas, you will stand a much better chance.

Sorry this is generic. If you want to speak with a former admissions officer from one of those schools, feel free to reach out to me.